{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/164599"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/164599","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Concretely-Efficient Multi-Key Homomorphic Secret Sharing and Applications","abstract":"Homomorphic secret sharing (HSS) is a powerful cryptographic primitive that enables efficient, low-communication secure computation without the use of fully homomorphic encryption. Public-key HSS is a well-known variant that supports inputs from multiple parties, but all parties must agree on a joint public key before any party can encode their inputs, requiring extra rounds of communication in applications. Recently, Couteau et al. (EUROCRYPT 2025) constructed multi-key HSS (MKHSS)—a new primitive which allows parties to encode their inputs under independent keys—under the DCR assumption. MKHSS assumes only a reusable common reference string, without the need for prior interactions between parties or a public-key infrastructure. In this paper, we construct and implement the first concretely-efficient MKHSS scheme under the same assumptions used by Couteau et al. Using an algorithmic insight that reduces the largest modulus in Couteau et al. from N⁴ to N², our optimized implementation can homomorphically multiply inputs in 5.0 milliseconds—while an implementation of Couteau et al. requires 224.6 milliseconds—thereby achieving a 45× speedup. A powerful application of MKHSS is to realize attribute-based non-interactive key exchange (ANIKE), which generalizes password-based key exchange (PAKE) to arbitrary attribute policies. ANIKE is currently only known from MKHSS. We use our implementation to evaluate the first concretely-efficient ANIKE schemes for a range of practically useful policies. Using our implementation, two parties can perform a geolocation-based key exchange in 1.65 seconds and a fuzzy PAKE on an 8-word passphrase in 7.59 seconds for realistic parameters, on a single core. Compared to using Couteau et al., which requires 62.5 and 253 seconds, we achieve 38× and 33× speedups, respectively.","abstract_html":"Homomorphic secret sharing (HSS) is a powerful cryptographic primitive that enables efficient, low-communication secure computation without the use of fully homomorphic encryption. Public-key HSS is a well-known variant that supports inputs from multiple parties, but all parties must agree on a joint public key before any party can encode their inputs, requiring extra rounds of communication in applications. Recently, Couteau et al. (EUROCRYPT 2025) constructed multi-key HSS (MKHSS)—a new primitive which allows parties to encode their inputs under independent keys—under the DCR assumption. MKHSS assumes only a reusable common reference string, without the need for prior interactions between parties or a public-key infrastructure. In this paper, we construct and implement the first concretely-efficient MKHSS scheme under the same assumptions used by Couteau et al. Using an algorithmic insight that reduces the largest modulus in Couteau et al. from N⁴ to N², our optimized implementation can homomorphically multiply inputs in 5.0 milliseconds—while an implementation of Couteau et al. requires 224.6 milliseconds—thereby achieving a 45× speedup. A powerful application of MKHSS is to realize attribute-based non-interactive key exchange (ANIKE), which generalizes password-based key exchange (PAKE) to arbitrary attribute policies. ANIKE is currently only known from MKHSS. We use our implementation to evaluate the first concretely-efficient ANIKE schemes for a range of practically useful policies. Using our implementation, two parties can perform a geolocation-based key exchange in 1.65 seconds and a fuzzy PAKE on an 8-word passphrase in 7.59 seconds for realistic parameters, on a single core. Compared to using Couteau et al., which requires 62.5 and 253 seconds, we achieve 38× and 33× speedups, respectively.","abstract_has_math":false,"creators":["He, Kaiwen"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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Public-key HSS is a well-known variant that supports inputs from multiple parties, but all parties must agree on a joint public key before any party can encode their inputs, requiring extra rounds of communication in applications. Recently, Couteau et al. (EUROCRYPT 2025) constructed multi-key HSS (MKHSS)—a new primitive which allows parties to encode their inputs under independent keys—under the DCR assumption. MKHSS assumes only a reusable common reference string, without the need for prior interactions between parties or a public-key infrastructure. In this paper, we construct and implement the first concretely-efficient MKHSS scheme under the same assumptions used by Couteau et al. Using an algorithmic insight that reduces the largest modulus in Couteau et al. from N⁴ to N², our optimized implementation can homomorphically multiply inputs in 5.0 milliseconds—while an implementation of Couteau et al. requires 224.6 milliseconds—thereby achieving a 45× speedup. A powerful application of MKHSS is to realize attribute-based non-interactive key exchange (ANIKE), which generalizes password-based key exchange (PAKE) to arbitrary attribute policies. ANIKE is currently only known from MKHSS. We use our implementation to evaluate the first concretely-efficient ANIKE schemes for a range of practically useful policies. Using our implementation, two parties can perform a geolocation-based key exchange in 1.65 seconds and a fuzzy PAKE on an 8-word passphrase in 7.59 seconds for realistic parameters, on a single core. Compared to using Couteau et al., which requires 62.5 and 253 seconds, we achieve 38× and 33× speedups, respectively."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["S.M."]},{"key":"dc:title","label":"Title","values":["Concretely-Efficient Multi-Key Homomorphic Secret Sharing and Applications"]}]}],"canonical_facts":{"dc:contributor.advisor":["Devadas, Srinivas"],"dc:contributor.department":["Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science"],"dc:creator":["He, Kaiwen"],"dc:date.accessioned":["2026-01-20T19:47:52Z"],"dc:date.available":["2026-01-20T19:47:52Z"],"dc:date.issued":["2025-09"],"dc:description.abstract":["Homomorphic secret sharing (HSS) is a powerful cryptographic primitive that enables efficient, low-communication secure computation without the use of fully homomorphic encryption. Public-key HSS is a well-known variant that supports inputs from multiple parties, but all parties must agree on a joint public key before any party can encode their inputs, requiring extra rounds of communication in applications. Recently, Couteau et al. (EUROCRYPT 2025) constructed multi-key HSS (MKHSS)—a new primitive which allows parties to encode their inputs under independent keys—under the DCR assumption. MKHSS assumes only a reusable common reference string, without the need for prior interactions between parties or a public-key infrastructure. In this paper, we construct and implement the first concretely-efficient MKHSS scheme under the same assumptions used by Couteau et al. Using an algorithmic insight that reduces the largest modulus in Couteau et al. from N⁴ to N², our optimized implementation can homomorphically multiply inputs in 5.0 milliseconds—while an implementation of Couteau et al. requires 224.6 milliseconds—thereby achieving a 45× speedup. A powerful application of MKHSS is to realize attribute-based non-interactive key exchange (ANIKE), which generalizes password-based key exchange (PAKE) to arbitrary attribute policies. ANIKE is currently only known from MKHSS. We use our implementation to evaluate the first concretely-efficient ANIKE schemes for a range of practically useful policies. Using our implementation, two parties can perform a geolocation-based key exchange in 1.65 seconds and a fuzzy PAKE on an 8-word passphrase in 7.59 seconds for realistic parameters, on a single core. Compared to using Couteau et al., which requires 62.5 and 253 seconds, we achieve 38× and 33× speedups, respectively."],"dc:description.degree":["S.M."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/164599"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Concretely-Efficient Multi-Key Homomorphic Secret Sharing and Applications"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Science in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:20Z"}